We propose a Non-Intrusive (or reference-free) Audio Clarity index (NIAC), inspired from previous works on image sharpness and defined as the sensitivity of the spectrogram sparsity to a convolution of the audio signal with a white noise. A closed-form formula is provided, which only involves the signal itself and very little parameter setting. Tested in various noise and reverberation conditions, the NIAC exhibits a high correlation with the well-established Speech Transmission Index, both for speech and music. It can also be used as a clarity criterion to drive sound enhancement algorithms. We propose a NIAC-based source separation algorithm, and show that its performance is comparable to that of a state-of-the-art algorithm, FastICA.